Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction
Department of Liberal Arts, Gyeongnam National University of Science and Technology, Jinju-Si 600-758, Gyeongsangnam-do, Korea
Symmetry 2019, 11(12), 1502; https://doi.org/10.3390/sym11121502
Received: 11 November 2019 / Revised: 4 December 2019 / Accepted: 9 December 2019 / Published: 11 December 2019
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a norm solution of the problems, which solves a certain hierarchical variational inequality.
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Keywords:
extragradient method; variational inequality; fixed point; pseudocontractions; sequentially weak continuity
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MDPI and ACS Style
Cho, S.Y. Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction. Symmetry 2019, 11, 1502.
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